During the transfer of many particulate materials, for example by means such as conveyor belts, considerable quantity of dust is generated which is unacceptable due to health and environmental hazards and also from a point of view of significant material losses. The known methods of wetting the surfaces of the material to be conveyed only partially eliminate dusting, since during the travel of the material, unwetted surfaces are continuously exposed resulting in further dusting. The present invention is directed to a system where during the travel of the dusty material the material is contacted with a dust controlling agent, for example water or an organic wetting agent, while the material being conveyed is simultaneously mixed or inverted through the application of a combination of plows and baffles located above the conveyor belt. The system of the invention not only significantly reduces the hazards associated with dusting, but also allows transport of dusty materials without encountering material losses. The system of the present invention can also be utilized to mix two or more nondusting particulate materials during conveying through the unique positioning of a combination of plows and baffles creating a material inverting system which is preferably located above the top surface of the conveyor belt.